Answer:
a. P(X ≤ 5) = 0.999
b. P(X > λ+λ) = P(X > 2) = 0.080
Step-by-step explanation:
We model this randome variable with a Poisson distribution, with parameter λ=1.
We have to calculate, using this distribution, P(X ≤ 5).
The probability of k pipeline failures can be calculated with the following equation:
[tex]P(k)=\lambda^{k} \cdot e^{-\lambda}/k!=1^{k} \cdot e^{-1}/k!=e^{-1}/k![/tex]
Then, we can calculate P(X ≤ 5) as:
[tex]P(X\leq5)=P(0)+P(1)+P(2)+P(4)+P(5)\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\P(3)=1^{3} \cdot e^{-1}/3!=1*0.3679/6=0.061\\\\P(4)=1^{4} \cdot e^{-1}/4!=1*0.3679/24=0.015\\\\P(5)=1^{5} \cdot e^{-1}/5!=1*0.3679/120=0.003\\\\\\P(X\leq5)=0.368+0.368+0.184+0.061+0.015+0.003=0.999[/tex]
The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as:
[tex]P(X>2)=1-(P(0)+P(1)+P(2))\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\\\P(X>2)=1-(0.368+0.368+0.184)=1-0.920=0.080[/tex]
Danessa needs to compare the area of one large circle with a diameter of 8 to the total area of 2 smalle
diameter one-half that of the large circle.
Which statements about the areas are true? Select three options.
The area of the large circle is 16
The area of one small circle is 4
The area of one small circle will be one-half of the area of the large circle.
The total area of the two small circles will equal that of the large circle
The total area of the two small circles will be one-half of the area of the large circle
Answer:
The area of the large circle is 16π
The area of one small circle is 4π
The total area of the two small circles will be one-half of the area of the large circle
Step by step explanation:
Area if circle = πr²
area of one large circle with a diameter of 8:
r = diameter/2 = 8/2 = 4
Area = π×4² = 16π
total area of 2 smaller diameter one-half that of the large circle.
Area = πr²
Diameter of small circle = 1/2(bigger circle diameter)
Diameter = 8/2 = 4
radius = 4/2 = 2
Area of one small circle = π×(2)² = 4π
Total Area of Two smaller circles= 2(4π) = 8π
Area of two smaller circle = 1/2(area of bigger circle) = 1/2(16π) 8π
Therefore, based on the answer:
The area of the large circle is 16π
The area of one small circle is 4π
The total area of the two small circles will be one-half of the area of the large circle
Answer:
The area of the large circle is 16 pi.
The area of one small circle is 4 pi.
The total area of the two small circles will be one-half of the area of the large circle.
Step-by-step explanation:
To shorten this down for ya lazy people like me the answers are 1, 2, and 5!!!
I got this right on my UNit test review!!!!!
I hope this helps!!!!!!
The pitcher releases the ball at the highest point in the curve, and the catcher is located at the y-axis. According to the table, how high is the ball when it reaches the catcher?
Answer: 2.5 ft
Step-by-step explanation:
Ok, we know that the catcher is located in the y-axis.
As you know, the y-axis cuts the x-axis at x = 0, so the catcher is located at x = 0.
To see the heigth of the ball at x = 0 we can see the table, where we can see that when x = 0, f(x) = 2.5 ft
Then the correct option is the second one, 2.5 ft.
Answer:
The answer is A. 2.5
The first option
Step-by-step explanation:
If we look at the question you'll see this phrase "X represents the horizontal distance the ball travels in feet" and "f(x) represents the height of the ball in feet."
The question is "The pitcher releases the ball at the highest point in the curve, and the catcher is located at the y-axis. According to the table, how high is the ball when it reaches the catcher?" the underlined words are your clue.
When the graph hit zero, its hit its mark "The catcher" it REACHES the catcher.
so, alas, the answer is 2.5 ft
The base of a solid right pyramid is a square with an edge
length of n units. The height of the pyramid is n - 1 units.
Which expression represents the volume of the pyramid?
on(n − 1) units
o zn(n − 1)2 units
o {n?(n − 1) units 3
on(n − 1) units
(n-1)
n
Answer:
These are all right answers, just pick the one that matches an answer choice
n^2 * (n-1)/3
(n^3-n^2)/3
((n-1)n^2)/3
Step-by-step explanation:
The general area for a square pyramid is base * height/3
Since we know the edge is n units, we can subsitute the base for:
n*n = n^2 = b
The height is n-1, so lets plug that into the formula too:
n^2 * (n-1)/3
Its a bit hard to tell what the answer choices are, since your formatting is a bit strange, So in the answer section, I will list a couple of different expressions that are all equal, so that I get the right answer choice included.
Question: A biotechnology firm is planning its investment strategy for future products and research labs. A poll found that 14% of a random sample of 1043 adults approved of attempts to clone a human. Use this information to complete arts a through e.
a) Find the margin of error for this poll if we want 95% confidence in our estimate of the percent of adults who approve of the cloning humans.
ME = ____ (Round to three decimal places as needed.)
b) Explain what that margin of error means. (Select One.)
i) The pollsters are 95% confident that the margin of error contains the true proportion of adults who approve of attempts to clone a human.
ii) The margin of error is the value that should be subtracted from the 95% confidence level to obtain the pollsters� true confidence level.
iii) The margin of error is width of the confidence interval that contains the true proportion of adults who approve of attempts to clone a human.
iv) The pollsters are 95% confident that the true proportion of adults who approve of attempts to clone a human is within the margin of error of the estimated 14%.
c) If we only need to be 99% confident, will the margin of error be larger or smaller?
i) A 99% confidence interval requires a smaller margin of error. A wider interval leads to decreased confidence.
ii) A 99% confidence interval requires a larger margin of error. In order to increase confidence, the interval must be narrower.
iii) A 99% confidence interval requires a smaller margin of error. A narrower interval leads to decreased confidence.
iv) A 99% confidence interval requires a larger margin of error. In order to increase confidence, the interval must be wider.
d) Find that margin of error.
ME = ___ (Round to three decimal places as needed.)
e) In general, if all other aspects of the situation remain the same, would smaller samples produce smaller or larger margins of error?
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
a) Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 1043
p = 14% = 14/100 = 0.14
q = 1 - 0.14 = 0.86
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for a confidence level of 95% is 1.96
Therefore, margin of error is 1.96√(0.14)(0.86)/1043
Margin of error = 0.021
b) i) The pollsters are 95% confident that the margin of error contains the true proportion of adults who approve of attempts to clone a human.
c) iv) A 99% confidence interval requires a larger margin of error. In order to increase confidence, the interval must be wider.
d) The z score for 99% confidence interval is 2.58
margin of error is 2.58√(0.14)(0.86)/1043
Margin of error = 0.028
e) smaller samples would produce smaller margins of error.
Read the problem and decide whether it has too much or too little
information,
Every day, Ellie the Elephant eats 150 pounds of hay, eats 200
pounds of fruit, and drinks 50 gallons of water. How many gallons
of water does she drink each week?
A. too much
B. too little
Answer:
A. too much
Step-by-step explanation:
If we are only looking for how much water she drinks, we do not need to know the amount of hay or the amount of fruit
Administrators want to understand how currently enrolled students are placing into their current math class. They randomly choose five math courses and ask the instructors to post a survey on their Canvas site for students to complete within the first week of class. The administrators will calculate the proportion of students that placed into their math class by their high school GPA..
a) What is the population of interest?
b) What is the population parameter of interest?
c) What is the sampling frame?
d) Describe the sample.
e) What type of sampling method was used for this study?
f) Who was possibly left out of this study?!
Answer:
Step-by-step explanation:
a) What is the population of interest?
The population of interest are college students
b) What is the population parameter of interest?
The population parameter is an average value on how currently enrolled students are placing into their current math class.
c) What is the sampling frame?
Identify currently enrolled students
d) Describe the sample.
The sample will be based on a representative sample that suit the administrators needs or specifically approach individuals with these certain characteristics.
e) What type of sampling method was used for this study?
Judgment or purposive sampling
f) Who was possibly left out of this study?
Translate “ the sum of x and one- half into a mathematical expression
Hey!!!!
Question:The sum of X and one half Answer:. X +1/2Hope it helps.....
Good luck on your assignment
__________________________________________
Suppose that we want to estimate the mean reading speed of second graders. The random sample of students' reading speeds we choose has a mean of 31.6 words per minute and a standard deviation of 2.4 words per minute. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean. (In the table, Z refers to a variable having a standard normal distribution, and t refers to a variable having a t distribution.) Sampling Scenario could use either Zort unclear (1) The sample has size 100, and it is from a non-normally distributed population with a known standard deviation of 2.6. (2) The sample has size 75, and it is from a non-normally distributed population. (3) The sample has size 12, and it is from a population with a distribution about which we know very little. (4) The sample has size 14, and it is from a normally distributed population with a known standard deviation of 2.6. (5) The sample has size 16, and it is from a normally distributed population with unknown standard deviation.
Answer:
Step-by-step explanation:
Hello!
Given the variable
X: reading speed of a second-grader. (words per minute)
From a random sample of second-grader the mean and standard deviation were:
X[bar]= 31.6 words per minute
S= 2.4 words per minute
To study the population mean (μ) you have the following sampling scenarios and need to choose the correct statistic.
Sampling scenarios:
(1) The sample has size 100, and it is from a non-normally distributed population with a known standard deviation of 2.6.
For this scenario you have to remember the Central Limit Theorem. The variable of study has a non-normal distribution but the sample is large enough (As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation) you can approximate the distribution of the sample mean to normal: X[bar]≈N(μ;σ²/n); Then it is valid to use an approximation to the standard normal distribution to make inference statements about the population mean.
Statistic: Z
(2) The sample has size 75, and it is from a non-normally distributed population.
Same explanation as the statement before, except that the population variance is unknown. Since the distribution is already an approximation you can use its estimation (sample variance) for the statistic. (It would be less accurate than using the population variance but still valid)
Statistic: Z
(3) The sample has size 12, and it is from a population with a distribution about which we know very little.
To use a student's t the population needs to have a normal distribution, which is not the case, same goes for the standard normal.
To apply the central Limit Theorem you need a sample size equal or greater to 30, this is not the case.
For this sampling example neither distribution is applicable.
(4) The sample has size 14, and it is from a normally distributed population with a known standard deviation of 2.6.
The population has a normal distribution and the population standard deviation is known. The sample size is rather small but it isn't an impediment to apply the standard normal distribution. Also, even tough the population standard deviation is known, a student t is also applicable. In this case both statistics are a viable option.
Statistic: Z or t
(5) The sample has size 16, and it is from a normally distributed population with unknown standard deviation.
The population has a normal distribution, with unknown population standard deviation and the sample size is rather small. You can use a Student t to infer over the population mean.
Statistic: t
I hope this helps!
What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)?
Answer:
hope this helps you
In a recent survey about what food was your favorite take-out, it was determined that 40% of students preferred pizza, 32% of students preferred cheeseburgers, and 28% of students preferred tacos. Based of this data, how many students out of 1,800 chose cheeseburgers?
Answer:
576 students choose cheeseburgers
Step-by-step explanation:
Given: In a survey, it was determined that 40% of students preferred pizza, 32% of students preferred cheeseburgers, and 28% of students preferred tacos.
To find: Number of students out of 1800 who choose cheeseburgers
Solution:
Percentage of students who preferred cheeseburgers = 32%
Total number of students = 1800
Number of students out of 1800 who choose cheeseburgers = [tex]\frac{32}{100}(1800)=576[/tex]
find the slope of a line perpendicular to the graph of the equation y=-3x
Answer:
1/3
Step-by-step explanation:
The slope of a perpendicular line is always the negative reciprocal of the slope of the original line.
-1/-3 = 1/3
Marine scientists categorize signature whistles of bottlenose dolphins by typelong dash—type a, type b, type c, etc. In one study of a sample of 185 whistles emitted from bottlenose dolphins in captivity, 100100 were categorized as type a whistles. a. Estimate the true proportion of bottlenose dolphin signature whistles that are type a whistles. Use a 9595% confidence interval.
Answer:
The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 185, \pi = \frac{100}{185} = 0.5405[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 - 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.4687[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 + 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.6123[/tex]
The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).
What is the value of the expression below?
Answer:
(7÷2)-(4.5*3)+8
(3.5)-(13.5)+8
3.5-5.5=-2
Na którym rysunku narysowano symetralną odcinka KL?
Która z tych liter nie ma osii symetrii?
Answer:
- Only Drawing D has KL being a symmetrical segment.
- Drawings A, B and C have no axis of symmetry.
- Tylko rysunek D ma KL będący segmentem symetrycznym.
- Rysunki A, B i C nie mają osi symetrii.
Step-by-step explanation:
English Translation
In which drawing was the symmetrical segment of KL drawn? Which of these letters has no axis of symmetry?
Solution
The attached image to the question is presented in the attached image to this Solution.
Symmetry is a concept where a figure/shape has half of its part being a mirror image of the other part.
About the line or axis of symmetry, the structure or figure can be rotated at right angles or whole number multiples of right angles and the resulting structure is still the same as the one we started with.
Of the 4 drawings, only drawing D satisfies this conditions/criteria. And Hence, it is the only drawing amongst the four with an axis of symmetry.
In Polish/Po polsku
Załączony obraz do pytania jest przedstawiony na załączonym obrazku do tego rozwiązania.
Symetria to koncepcja, w której figura / kształt ma połowę swojej części stanowiącą odbicie lustrzane drugiej części.
W odniesieniu do linii lub osi symetrii, strukturę lub figurę można obracać pod kątem prostym lub wielokrotności liczby całkowitej pod kątem prostym, a wynikowa struktura jest nadal taka sama jak ta, od której zaczęliśmy.
Z 4 rysunków tylko rysunek D spełnia te warunki / kryteria. I dlatego jest to jedyny rysunek wśród czterech z osią symetrii.
Hope this Helps!!!
Mam nadzieję że to pomoże!!!
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. What is the margin of error for a 95% confidence interval for the population mean
Answer:
The margin of error for a 95% confidence interval for the population mean is of 1.05 years.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population(square root of the variance) and n is the size of the sample.
What is the margin of error for a 95% confidence interval for the population mean
36 students, so [tex]n = 36[/tex]
Variance of 10.24, so [tex]\sigma = \sqrt{10.24} = 3.2[/tex]
[tex]M = 1.96*\frac{3.2}{\sqrt{36}} = 1.05[/tex]
The margin of error for a 95% confidence interval for the population mean is of 1.05 years.
A pump discharges 278 gallons of water in 3.5 minutes. How long would it take to empty a container with 750 gallons? Round up to the nearest minute
Find the value of x and y in the parallelogram below.
Answer:
x=4 and y = 12
Step-by-step explanation:
A diagonal of a parallelogram cuts the other diagonal in exactly 2 equal parts. So, we can say that x+12 = 16. That would give us x=4. And, we can say that 3y-14 = 22. If we solve for y, we get y = 12.
Graph: y +2=
(x + 4)
ty
Y
4
2
8
-6
-4
-2
2
4
-2
-4
-6
Answer:
see below
Step-by-step explanation:
The point-slope form of the equation of a line is ...
y -h = m(x -k)
for a line with slope m through point (h, k).
Comparing this to the given equation, you see that ...
h = -2, m = 1, k = -4
The line has a slope of 1 and goes through the point (-4, -2). This information is useful for graphing.
__
You can also rearrange the equation to slope-intercept form by subtracting 2 from both sides.
y = x +2
This has a slope of 1 and crosses the y-axis at y=2. It graphs the same as the above.
Three roots of a fifth degree polynomial function f(x) are -2, 2, and 4 + i. Which statement describes the number and nature of
all roots for this function?
Of(x) has two real roots and one imaginary root.
f(x) has three real roots.
f(x) has five real roots.
Of(x) has three real roots and two imaginary roots.
We know that imaginary roots always come in pairs, so we already know 4 solutions
-2, 2, 4 + i and a pair of 4 + i
Since imaginary roots always come in pairs we wont have more than 2 imaginary roots, since its a fifth degree root and we can only have 5 roots
So for sure, we will have 3 real roots and 2 imaginary roots
Last option, f(x) has three real roots and two imaginary roots
Answer: ITS D (f(x) has three real roots and two imaginary roots)
Alan found 4 marbles to add to the 5 marbles in his collection. Then, he went to the store and tripled the number of marbles he had.
Answer:
27 Marbles
Step-by-step explanation:
Alan first had 5 marbles, and then added 4 to the collection.
5 + 4 = 9
He went to the store and tripled the number of marbles he had.
9 x 3 = 27
Hence, he now has 27 marbles.
Answer: think for yourself
in 2010 a tree was 8 feet tall 2011 it was 14 feet tall write the equation how many feet the tree grew
Answer:
14 ft - 8 ft = 6 ft
Step-by-step explanation:
You basically just need to subtract it! :)
Question 4 of 10
2 Points
Match each type of consumer influence with an example of that influence in
action.
Choosing a red and black
sweater because those
are school colors
Price
Wearing a Santa Claus
sweater because
Christmas is approaching
Cultural
Buying a sweater after
winter is over because of a
clearance sale N
TL
TA
Peer pressure
HIRD
BEBE
L
EHELE
Answer:
1. Peer pressure: Choosing a red and black sweater because those are school colors.
2. Cultural: Wearing a Santa Claus
sweater because Christmas is approaching.
3. Price: Buying a sweater after winter is over because of a clearance sale.
Step-by-step explanation:
Peer pressure is a direct influence from groups or institutions an individual belong to.
Cultural elements relates to the customs, beliefs and behavior of a group of people in a society.
Price is the amount of money paid by an individual or organizations in acquiring goods and services.
Find the perimeter of a rectangle with a length of 32 feet and a width of 56 feet
Answer:
Perimeter= 176
Step-by-step explanation:
If one length is 32, then the length parallel to it, is also 32. Meaning the side lengths altogether equal 64. The width, is 56, so then the width parallel to it is also 56. This means the width of each equals 112 altogether.
64+112=176.
P= 176 feet
Hey!!!!
Here's your answer
Solution:
Length(l)=32 feet
Breadth(b)=56 feet
Now,
Perimeter of rectangle=2(l+b)
=2(32+56)
=2*88
=176
So the right answer is 176 feet
Hope it helps ...
Good luck on your assignment
What is the zero of the function below?
f(1) = 3v1 + 3 - 6
Answer:
v1 = 1
Step-by-step explanation:
Solve for v1:
3 v1 - 3 = 0
Add 3 to both sides:
3 v1 + (3 - 3) = 3
3 - 3 = 0:
3 v1 = 3
Divide both sides of 3 v1 = 3 by 3:
(3 v1)/3 = 3/3
3/3 = 1:
v1 = 3/3
3/3 = 1:
Answer: v1 = 1
A patient is using Humulin insulin U100, the patient is to use 35units three times a day, how many milliliters will be used each day
Answer:
Step-by-step explanation:
(35 units three times a day) comes out to (35 units / day)(3 times per day), or
105 units per day
"Find the coefficient of determination given that the correlation coefficient = -.39"
(Give your answer as a decimal rounded to the ten thousandth decimal place.)
Answer:
[tex] r = -0.39[/tex]
And the determination coeffcient is just the correlation coeffcient square and we got:
[tex] R = r^2 = (-0.39)^2 =0.1521[/tex]
And rounded to the nearest tenth thousand would be 0.1521
Step-by-step explanation:
The correlation coefficient is a measure of variability and is given by this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
For this case we have
[tex] r = -0.39[/tex]
And the determination coeffcient is just the correlation coeffcient square and we got:
[tex] R = r^2 = (-0.39)^2 =0.1521[/tex]
And rounded to the nearest tenth thousand would be 0.1521
what’s the working out to this question as i know the answer is 2.94cm squared but the working out is wrong!
Answer:
2.94
Step-by-step explanation:
A = 6a²
6 × .7² = 2.94
.7 × .7 = .49
6 × .7 = 2.94
[tex] a = 6a {}^{2} [/tex]
a is the side
area -6 x 0.7
Employees from Company A and Company B both receive annual bonuses. What information would you need to test the claim that the difference in annual bonuses is greater than $100 at the 0.05 level of significance? Write out the hypothesis and explain the testing procedure.
Answer:
Step-by-step explanation:
This is a test of the mean difference between 2 independent groups or populations.
Let μ1 be the mean annual bonus of Company A's employees and μ2 be the mean annual bonus of Company B's employees.
The random variable is μ1 - μ2 = difference in the mean annual bonus of Company A's employees and the mean annual bonus of Company B's employees
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 ≤ μ2 H0 : μ1 - μ2 ≤ 100
The alternative hypothesis is
H1 : μ1 > μ2 H1 : μ1 - μ2 > 100
This is a right tailed test because of the inequality sign at the alternative hypothesis. We need to take samples of annual bonuses from both company's employees and find the averages. Then we would determine the test statistic as well as the p value. We would use the p value with the level of significance to make decisions
A frozen yogurt shop offers scoops in cake cone, waffle cones, or cups. You can get vanilla, chocolate, strawberry, pistachio, or coffee flavored frozen yogurt. If you order a single scoop, how many outcomes are in the sample space?
Answer:
15 possible outcomes
Step-by-step explanation:
Given;
A frozen yogurt shop offers scoops in cake cone, waffle cones, or cups.
N1 = 3 possible options
You can get vanilla, chocolate, strawberry, pistachio, or coffee flavored frozen yogurt.
N2 = 5 possible options
The total number of possible outcomes in the sample space when you order a scoop of yogurt is the product of the available options;
N = N1 × N2 = 3 × 5
N = 15 possible outcomes
A chicken weighs t lbs. It needs to be cooked for 20 minutes per lb plus an extra 15 minutes. What is the total cooking time? Is this the correct written expression: 15t + 20? Why or why not?
Answer:
Total cooking time = 20t + 15
The expression 15t + 20 is wrong.
Step-by-step explanation:
weight of chicken = t lbs
cook time per lb = 20 minutes
This means that:
1 lb weight requires a cooking time of 20 minutes
1 lb = 20 minutes
∴ t lbs = 20 × t = 20t minutes.
We were also told that each chicken required an extra cooking time of 15 minutes, in addition to the total cooking time due to the weight. Therefore, the total cooking time is calculated thus:
Total cooking time = cooking time due to weight + 15 minutes
Total cooking time = 20t + 15
Hence the expression 15t + 20 is wrong, due to the explanation given above.
